Part 3: QUANTUM WAVE SOURCES page 3

 

3.5. Wave Sources in Two- and Three-Dimensional Traditional Mediums

Figure 7A illustrates a central wave source within a two-dimensional medium. The waves within this medium are transversal. The central wave source has a diameter of ½ a wavelength and is emitting waves in all directions out of this central source with the same wavelength. All the waves emerging from the center are not shown in Figure 7A. If they were to be shown, the two-dimensional wave source would look like it does in Figure 1. Imagine that in the two-dimensional wave source of Figure 7A, waves smoothly and continuously fill the gap between these two waves, as shown in Figure 7A. I can create all of these waves that fill the gap by rotating one of those waves into the other. Each infinitesimal rotation would represent another wave being emitted from the central wave source.

Figure 7B represents a wave source in a two-dimensional medium also emitting waves in all directions in this medium. I did extend two waves represented there into two more waves with reverse amplitude. Notice that these waves are still wave sources but are only emitting waves in one direction, as opposed to the central wave source, which is emitting waves in all directions away from it. All the wave sources represented are essentially waves with a minimum of ½ a wavelength.

Transversal waves in traditional mediums can only exist two-dimensionally. In Figure 7C, I show a single slice of a central two-dimensional central wave source. Of course, there are two waves that are moving outward in opposite directions. This is represented by the double-sided arrow. To represent a three-dimensional central wave source, I need to show waves moving away from this central wave source in a direction that is perpendicular to this double-sided arrow in Figure 7C. I do this by rotating 90 degrees the two waves that will be emitted from the wave source. I create these waves by rotation so I can maintain smoothness and continuity, as I explained earlier for Figure 7A. In Figure 7D, I show that the rotated waves are now moving upward. However, their amplitudes are the reverse of each other and they cancel each other. A wave source cannot be three-dimensional unless it truly is a source for waves emerging from it in all directions three-dimensionally. Because along one axis the waves I have shown cancel each other, there are no three-dimensional transversal wave sources in classical mediums.

If there are three-dimensional transversal wave sources, the following description must be satisfied. I select a point in a three-dimensional space. Next, I draw a straight line through this point. Finally, I put the center of the three-dimensional transversal wave source on this line. This line could pass through the point along any direction, and there should be wave pulses along both directions of the line that are moving away from this wave source’s central point. This description has wave pulses moving out from the center in all directions within a three-dimensional medium. Furthermore, all these wave pulses must join smoothly and continuously as they do in Figure 1, which is within a two-dimensional medium. They cannot cancel along any direction as they did in Figure 7D.

 

3.6. Three-Dimensional Transversal Wave Sources

In a previous section, I described the scenario of a pool with a central wave source and rings of wave fronts propagating away from the center. This wave source is a wave with ½ a wavelength emitting waves in all directions on the surface of the pool. Since this wave source is still a wave, it must be smooth and continuous in all directions. When I say smooth and continuous, I mean that I can draw a line along any path on this wave source’s surface so that the line would have no breaks and no corners. It is also important to note that if a wave source is a complete two-dimensional wave source, it will emit waves in all directions on a plane. Therefore, rings of wave fronts will propagate away from the central wave.

Of course, I cannot use a surface of a pool of water for a scenario to illustrate a three-dimensional transversal wave source. Indeed, I cannot use any traditional medium for this scenario. The reason for this, as I showed in the previous section, is that the amplitudes of a three-dimensional transversal wave source would cancel themselves out at least along one dimension. Consequently, I have to create a hypothetical medium to imbed this new kind of wave source. I will show that these new structures I create, three-dimensional transversal wave sources, can only exist with a quantified spin. Furthermore, these spins are quantified so that they correspond to an odd or an even number spin. I will later show how an odd spin and an even spin, respectively, predict fermions (quarks and leptons) and bosons (photons). Also, if this wave source has a spin that corresponds to an even number of wavelengths for a three-dimensional transversal wave source, then all the wave pulses’ amplitudes within this particle cancel each other. (This parallels fermions in particle physics. If any two fermions are identical, they can interfere in a manner so that the two are indistinguishably together. Hence, a single particle with an even spin would be created. These two identical particles would cancel each other’s amplitudes according to the Pauli exclusion principle, which is better known as “the Pauli exclusion principle”.) All of these results come from this new construct, without using traditional physics to derive my results. Although, I do use traditional physics for checking my results.

If a wave source is truly three-dimensional, three-dimensionally it should emit waves in all directions away from its center. This is difficult to do with three-dimensional transversal wave sources without waves canceling each other along at least one axis. If any wave pulses cancel along any axis, a three-dimensional wave source cannot be constructed. A three-dimensional transversal wave source must emit waves out away from its center in all directions without any canceling. This wave source must be smooth and continuous so that a straight or curved line can be drawn on it in any direction without crossing any breaks or corners.

To explain the three-dimensional transversal wave source, I describe a wave source as made of an indefinite number of one-directional wave pulses. (See Figure 8.) In my hypothetical medium, the waves' amplitudes add up in a reverse manner if they move in the opposite directions relative to each other. (See Rule 2 in Table 1.) When they are moving in the same direction, they add up normally. A central wave source has waves moving outwardly in all directions. Hence, a central wave source has pulses that move in opposite directions to each other. These pulses must have reverse amplitudes so they can add up constructively. I color-coded these pulses along with the arrows pointing in the direction in which each is moving. The black pulse and the red pulse are moving in opposite directions and their amplitudes are reversed. The same is true for the blue and green pulses. Therefore, the pulses' amplitudes add up constructively. Notice, I can take the red pulse in Figure 8A or Figure 8B and rotate it, and it will eventually coincide with the green, black, and blue pulses in turn. This means the pulses are components of a completely smooth and continuous wave.

Figure 8A lies on the Z, Y plane, and Figure 8B lies on the X, Y plane. I set the wave in 8B to be 90 degrees out of phase with the wave in 8A. Hence, the waves in 8A are flat (zero amplitude) when the waves in 8B are at maximum amplitude and vice versa. Furthermore, there is an indefinite number of waves, as in the waves in 8A and 8B, and they are waving in between the waves in 8A and 8B. In addition, the phases of the waves on these planes happen in a manner so that the closer the wave is to 8A’s wave, the more it is in phase with it. The same is true for the waves as they get closer to 8B’s wave. As a result, spin is created as all of these wave pulses wave or cycle through their phases. This approach allows the three-dimensional transversal wave source to exist without canceling amplitudes in any direction.

These wave pulses add up to create a wave front moving away from its center location in all directions. These pulses are essentially standing waves because, according to Rule 3 in Table 1, these pulses trap each other. All these wave pulses join smoothly and continuously, which satisfies Rule 6 of Table 1. Hence, there is a force that holds them together and does not let them fly apart in the direction outward from the center. Since they are standing waves, these wave pulses have zero velocity, but I do assign direction to them.

In Figure 9, I create Figures 9A through 9D by looking down in the negative Y axis direction of a three-dimensional transversal wave source like the one in Figure 8. Hence, I am looking down on the X, Z plane. In Figure 9A, the wave is at time (t = 1). In this image, U (up) means that there is a wave crest at the center with a direction to the left, and D (down) means there is a wave trough with a direction to the right. Parallel to the Z axis, the wave amplitudes are zero. I now stand at the center of Figure 9A facing the negative X axis direction and spin in a circle. I first see a pulse with up amplitude. As I continue to spin, this view would smoothly and continuously change to zero amplitude, then to down, and then back to zero amplitude. Finally, I would see the up amplitude where I started. While I spun in this complete circle, I would witness one complete wavelength. Therefore, the wave source presented in this figure has a 1 wavelength spin.

This wave source cycles through its phases. Figure 9B occurs at time (t = 2). At this time the wave source has spun so that in the negative Z axis direction, the amplitude is up; and in the positive Z axis direction, it is down. Along both directions parallel to the X axis, there is zero amplitude. The wave continues to rotate through Figures 9C and 9D. Finally, the wave will arrive back to Figure 9A. I refer to this wave as having spin 1 because its circumference encompasses one wavelength.

Since a wave source is still a wave, it must be smooth and it must fit like any quantum wave in a small region of space. As I spun in a complete circle, I observed how the amplitudes smoothly changed from up to down and back to up. During this observation, I viewed no part of the wave that was disconnected or had a corner. This is a requirement: that a wave source be smooth and continuous when all of its wave pulses fit together. In other words, viewing from the center and turning in any direction, I would see amplitudes of various wave pulses smoothly and continuously forming a single wave source. Therefore, these amplitudes must fit together along a circumference so that an up part of the wave source is a distance of ½ a wavelength away from a down part of the wave source in Figure 9. If I were to create other wave sources of this kind, they would have a spin that exist at integer wavelengths because their amplitudes have to go from up to down and back to up again. If not for this, the wave would not be continuous. In other words, all the crests and troughs have to smoothly fit together in a wave source. However, the diameter of the wave source would exist at ½ a wavelength, which is the length of each wave pulse. This agrees with elementary quantum theory, which requires that the minimum distance that any quantum may span be a distance of ½ a wavelength.

It is interesting that the structure defined requires a spin as the wave source vibrates. Indeed for spin 1, as each wave pulse in the structure vibrates, a corresponding spin occurs according to the relationship where one complete cycle of the frequency equals one complete rotation of the particle. Also, for spin 3 the relationship is that three complete cycles of the frequency equals one complete rotation of the particle. These are both linear relationships. These equations are such that a greater frequency results in a greater spin, or a lower frequency results in a lower spin. This should be a characteristic of fermions if they do have this structure (the three-dimensional transversal wave source) at their core. I state that the energy of the waves that I construct are given by

hf = E. _______________________________________________(1)

A wave is not a part of a wave. It is the total entity because the existence of one segment of the wave affects all the other parts. Therefore, it is the whole wave that is the wave. If you take away a part of the wave, you have a different wave, and it will act differently, too. Thus, a wave must be understood as a whole.